Finite Group Databasebeta

← #14668743

Subgroups — #14668743

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622853C212yesmaximal
2#13066741C214yesmaximal, complemented
3C11×#2297C211yesmaximal, characteristic
4C22×C11×#41C2211yescharacteristic
5C2×C11×#117C411yescharacteristic, complemented
6C22×C42×C11C411yescharacteristic, complemented
7C2×#66979—22no—
8C11×#391C412yescomplemented
9C11×#390C2212yes—
10C11×#386—22no—
11C4×C11×C22⋊C4—22no—
12#10622853—24no—
13#10622853C418yescomplemented
14C2×#66898—22no—
15C2×#66898C2214yes—
16C2×C11×#41—41no—
17C2×C11×#41—41no—
18C2×C11×#41—42no—
19C2×C11×#41C2×C414yes—
20C2×C11×#41D412yes—
21C2×C11×#41Q812yes—
22C22×Q8×C11C2×C411yescharacteristic
23C22×D4×C11D412yes—
24C22×D4×C11C2311yescharacteristic
25C23×C4×C11—21no—
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11D412yes—
28C11×#117—41no—
29C11×#117—41no—
30C2×C11×C4⋊C4C2×C412yes—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—24no—
33C2×C42×C11—21no—
34C2×C42×C11—21no—
35C2×C42×C11—42no—
36C2×C42×C11C2×C412yes—
37C2×C22⋊Dic11—24no—
38#66979—28no—
39#66979—44no—
40C2×C4⋊Dic11—42no—
41C2×C4×Dic11—42no—
42C11×#95—24no—
43#66898—28no—
44#66898—24no—
45#66898C2×C418yescomplemented
46#12581—111nomaximal, Sylow
47C24×C11C22⋊C411yescharacteristic
48C24×C11C2×D412yes—
49C11×#41—44no—
50C11×#41—44no—
51C11×#41—42no—
52C11×#41—42no—
53C11×#41—42no—
54C11×#41—42no—
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×Q8×C11C4212yes—
58C2×Q8×C11C4⋊C412yes—
59C2×D4×C11—42no—
60C2×D4×C11—42no—
61C2×D4×C11—41no—
62C2×D4×C11—41no—
63C2×D4×C11C22⋊C414yes—
64C2×D4×C11C4⋊C414yes—
65C2×D4×C11C22×C412yes—
66C2×D4×C11C2×D411yescharacteristic
67C2×D4×C11C2×Q811yescharacteristic
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—24no—
71C22×C4×C11—22no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—44no—
77C22×C4×C11—42no—
78C22×C4×C11C4212yes—
79C22×C4×C11C22⋊C414yes—
80C22×C4×C11C22⋊C412yes—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C4⋊C414yes—
83C22×C4×C11C4⋊C412yes—
84C22×C4×C11C22×C411yescharacteristic
85C22×Dic11—44no—
86C11×C4⋊C4—42no—
87C11×C22⋊C4—48no—
88C11×C22⋊C4—42no—
89C42×C11—42no—
90C42×C11—42no—
91C42×C11—41no—
92C42×C11—41no—
93C22⋊Dic11—28no—
94C22⋊Dic11—44no—
95C4⋊Dic11—48no—
96C4×Dic11—48no—
97C2×#410—112no—
98#2297D1111yescharacteristic
99#1393—114no—
100C23×C11—21no—
101C23×C11—22no—
102C23×C11—21no—
103C23×C11—22no—
104C23×C11—42no—
105C23×C11—44no—
106C23×C11#9512yes—
107C23×C11C2×C22⋊C412yes—
108C23×C11C2×C22⋊C411yescharacteristic
109C23×C11C2×C4⋊C412yes—
110Q8×C11—42no—
111Q8×C11—42no—
112D4×C11—44no—
113D4×C11—44no—
114D4×C11—42no—
115D4×C11—41no—
116D4×C11—41no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—24no—
122C2×C4×C11—24no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—24no—
126C2×C4×C11—24no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—24no—
130C2×C4×C11—42no—
131C2×C4×C11—48no—
132C2×C4×C11—42no—
133C2×C4×C11—44no—
134C2×C4×C11—42no—
135C2×C4×C11#9514yes—
136C2×C4×C11#9512yes—
137C2×C4×C11#9912yes—
138C2×C4×C11#9911yescharacteristic
139C2×C4×C11#9911yescharacteristic
140C2×C4×C11C2×C4211yescharacteristic
141C2×C4×C11C2×C4⋊C411yescharacteristic
142C2×Dic11—48no—
143C2×Dic11—88no—
144C22×#41C2×D1111yescharacteristic
145C2×#117—222no—
146C2×#117Dic1111yescharacteristic, complemented
147C22×C42Dic1111yescharacteristic, complemented
148#410—118no—
149#410—224no—
150C2×#99—114no—
151C2×#99—222no—
152#391Dic1112yescomplemented
153#390C2×D1112yes—
154#386—22no—
155C4×C22⋊C4—22no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11—42no—
161C22×C11—42no—
162C22×C11—42no—
163C22×C11—42no—
164C22×C11—42no—
165C22×C11—44no—
166C22×C11—82no—
167C22×C11C2×#9511yescharacteristic
168C22×C11C2×#9911yescharacteristic
169C22×C11C2×#9911yescharacteristic
170C4×C11—24no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—44no—
174C4×C11—82no—
175C4×C11#34212yes—
176C4×C11#34212yes—
177Dic11—88no—
178C2×#41—42no—
179C2×#41—41no—
180C2×#41—41no—
181C2×#41Dic2212yes—
182C2×#41C4×D1114yes—
183C2×#41D4412yes—
184C22×Q8C2×Dic1111yescharacteristic
185C22×D4C22⋊D1112yes—
186C22×D4C22×D1111yescharacteristic
187C23×C4—21no—
188C23×C4C2×Dic1111yescharacteristic
189C23×C4C22⋊D1112yes—
190#117—41no—
191#117—41no—
192#117—228no—
193#117—444no—
194C2×C4⋊C4—442no—
195C2×C4⋊C4C2×Dic1112yes—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—224no—
199C2×C42—21no—
200C2×C42—21no—
201C2×C42—42no—
202C2×C42—442no—
203C2×C42C2×Dic1112yes—
204#99—118no—
205#99—228no—
206#99—224no—
207#95—24no—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11—42no—
211C2×C11—42no—
212C2×C11—42no—
213C2×C11C2×#34211yescharacteristic
214C2×C11#212612yes—
215C24C22⋊Dic1111yescharacteristic
216C24C2×C22⋊D1112yes—
217#41—42no—
218#41—42no—
219#41—44no—
220#41—44no—
221#41—42no—
222#41—42no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×Q8C4×Dic1112yes—
226C2×Q8C4⋊Dic1112yes—
227C2×D4—41no—
228C2×D4—41no—
229C2×D4—42no—
230C2×D4—42no—
231C2×D4Dic11⋊C414yes—
232C2×D4(C2×D11)⋊C414yes—
233C2×D4C2×Dic2211yescharacteristic
234C2×D4C2×C4×D1112yes—
235C2×D4C2×D4411yescharacteristic
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—24no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—44no—
245C22×C4—42no—
246C22×C4—444no—
247C22×C4C4×Dic1112yes—
248C22×C4Dic11⋊C414yes—
249C22×C4C4⋊Dic1112yes—
250C22×C4(C2×D11)⋊C414yes—
251C22×C4C22⋊Dic1112yes—
252C22×C4C22⋊Dic1111yescharacteristic
253C22×C4C22×Dic1111yescharacteristic
254C4⋊C4—42no—
255C4⋊C4—448no—
256C22⋊C4—48no—
257C22⋊C4—42no—
258C22⋊C4—228no—
259C22⋊C4—444no—
260C42—42no—
261C42—42no—
262C42—41no—
263C42—41no—
264C42—448no—
265C11#1258111yescharacteristic, complemented, Sylow
266C23—21no—
267C23—21no—
268C23—22no—
269C23—22no—
270C23—42no—
271C23—44no—
272C23C11⋊#9512yes—
273C23C2×Dic11⋊C412yes—
274C23C2×(C2×D11)⋊C412yes—
275C23C2×C22⋊Dic1111yescharacteristic
276Q8—42no—
277Q8—42no—
278D4—44no—
279D4—44no—
280D4—41no—
281D4—42no—
282D4—41no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—24no—
296C2×C4—42no—
297C2×C4—48no—
298C2×C4—42no—
299C2×C4—44no—
300C2×C4—42no—
301C2×C4—448no—
302C2×C4—888no—
303C2×C4C11⋊#9514yes—
304C2×C4C11⋊#9512yes—
305C2×C4#6689811yescharacteristic
306C2×C4#6689812yes—
307C2×C4#6689811yescharacteristic
308C2×C4C2×C4×Dic1111yescharacteristic
309C2×C4C2×C4⋊Dic1111yescharacteristic
310C22—22no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—44no—
319C22—42no—
320C22—82no—
321C22C2×C11⋊#9511yescharacteristic
322C22C2×#6689811yescharacteristic
323C22C2×#6689811yescharacteristic
324C4—24no—
325C4—21no—
326C4—21no—
327C4—44no—
328C4—82no—
329C4—888no—
330C4#1062216412yes—
331C4#1062216412yes—
332C2—21no—
333C2—21no—
334C2—42no—
335C2—42no—
336C2—42no—
337C2C2×#1062216411yescharacteristic
338C2#1307028112yes—
subgroupG/H
centerC2×C4#66898
commutatorC2×C4×C11C2×C42
FrattiniC22×D4C22×D11
FittingC11×#2297C2
socleC22×C11C2×#99
prime radicalC22×C11×#41C22
cosocleC22×D4×C11C23
hypercenter#2297D11
hypocenterC11#12581
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ #2297

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13066741C2semidirect
5. C2×C11×#117C4semidirect
6. C22×C42×C11C4semidirect
8. C11×#391C4semidirect
13. #10622853C4semidirect
45. #66898C2×C4semidirect
146. C2×#117Dic11semidirect
147. C22×C42Dic11semidirect
152. #391Dic11semidirect
265. C11#12581semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106228532
#130667412
C11×#22972
#1258111